Applications of Continuous Mathematics to Computer Science

H.T. Nguyen and V. Kreinovich Applications of Continuous Mathematics to Computer Science "The book represents a fine state-of-the-art description of combinatorial optimization. The book presents not only a lot of well-known solutions but also a row of new results and demonstrates how to formulate and to answer original questions. The comprehensive book covers the scope of a normal textbook on combinatorial optimization and goes beyond the contents of such a book in several aspects, e.g.; this book contains complete proofs. To read this is very stimulating for all the researchers, practitioners, and students in combinatorial optimization."-OR-NEWS

• Preface. 1. Algorithm Complexity: Two Simple Examples. 2. Solving General Linear Functional Equations: An Application to Algorithm Complexity. 3. Program Testing: A Problem. 4. Optimal Program Testing. 5. Optimal Choice of a Penalty Function: Simplest Case of Algorithm Design. 6. Solving General Linear Differential Equations with Constant Coefficients: An Application to Constrained Optimization. 7. Simulated Annealing: `Smooth' (Local) Discrete Optimization. 8. Genetic Algorithms: `Non-Smooth' Discrete Optimization. 9. RISC Computer Architecture and Internet Growth: Two Applications of Extrapolation. 10. Systems of Differential Equations and Their Use in Computer-Related Extrapolation Problems. 11. Network Congestion: An Example of Non-Linear Extrapolation. 12. Neural Networks: A General Form of Non-Linear Extrapolation. 13. Expert Systems and the Basics of Fuzzy Logic. 14. Intelligent and Fuzzy Control. 15. Randomness, Chaos, and Fractals. A: Simulated Annealing Revisited. B: Software Cost Estimation. C: Electronic Engineering: How to Describe PN-Junctions. D: Log-Normal Distribution Justified: An Application to Computational Statistics. E: Optimal Robust Statistical Methods. F: How to Avoid Paralysis of Neural Networks. G: Estimating Computer Prices. H: Allocating Bandwidth on Computer Networks. I: Algorithm Complexity Revisited. J: How Can a Robot Avoid Obstacles: Case Study of Real-Time Optimization. K: Discounting in Robot Control: A Case Study of Dynamic Optimization. Index.